Jean-Luc Thiffeault

The final exam is on Thursday December 20 at 2:45pm. It will last 2 hours. The exam will consist of (about) 4 questions. You are responsible for all the material in the class, except as noted below, but the exam will lean heavily on the post-midterm parts.

Syllabus

Textbook

The textbook for the class is Nonlinear Dynamics and Chaos by Steven Strogatz (Second Edition).

Prerequisites

Homework

Every two weeks or so I will assign homework from the textbook and post it here.

HW 1 (Due Sept 25): 2.1: 1–4; 2.2: 1–4, 7, 10, 13; 2.3: 1, 4; 2.4: 1, 3, 6, 9; 2.5: 1, 2, 4, 6; 2.7: 1, 3. Solutions

HW 2 (Due Oct 9): 3.1: 1, 2; 3.2: 1, 2, 4; 3.3: 1 [except (d)]; 3.4: 1 (note: r x + 4x³), 2, 4, 5, 7, 10, 11, 15; 3.5: 2, 3, 6 [except (e)]; 3.6: 2, 4. Solutions

HW 3 (Due Oct 23): 3.7: 1–4. 5.1: 3–6, 9, 10; 5.2: 1–4, 7, 10, 11, 13. Solutions

HW 4 (Due Nov 6): 6.1: 1, 2, 4, 6; 6.2: 2; 6.3: 1, 2, 4, 5, 9 (except (e)), 11, 13; 6.4: 3, 4. [6.3.2, 6.3.5: OK in this case to assume centers persist.] Solutions

HW 5 (Due Nov 20): 6.5: 1, 2, 3, 11, 19; 6.7: 2 [except the 'reversible' question in (c)]; 6.8: 1, 3, 4, 5, 6, 8; 7.1: 1, 4, 8; 7.2: 2, 6, 10, 14; 7.3: 1, 3, 4. Solutions

HW 6 (Due Dec 11): 9.2: 1, 2 [except 'stiffer challenge']; 10.1: 10, 11; 10.3: 1, 4, 5, 7. Solutions [Correction: 10.1.11 x=0 should be unstable.]

Canvas

We'll use Canvas discussions about the class and related topics. Feel free to post questions and answers there about homeworks and exams, logistics, or relevant interesting things you found on the web.

Schedule of Topics

lecture	date	sections	topic
1	09/06	1	Introduction
2	09/11	2.1–2.4	One-dimensional ODEs
3	09/13	2.5–2.8	Existence and uniqueness
4	09/18	–	Modeling hagfish slime [Matlab code]
5	09/20	–	Hagfish (cont'd)
6	09/25	3.1	Saddle-node bifurcations
7	09/27	3.2–3.4	Transcritical and pitchfork bifurcations
8	10/02	3.5	Overdamped bead
9	10/04	3.6	Imperfect bifurcations; catastrophes
10	10/09	3.7	Insect outbreak
11	10/11	5.1	Two-dimensional linear flows
12	10/16	5.2	Two-dimensional linear flows (cont'd)
13	10/18	5.2	Two-dimensional linear flows (finish)
14	10/23	6.1–6.2	Phase plane
15	10/25	6.3–6.4	Linearization; Lotka–Volterra model
–	10/30	–	MIDTERM [mean 70%; solutions]
16	11/01	6.4–6.5	Lotka–Volterra model; Conservative systems
17	11/06	6.7	Pendulum
18	11/08	6.8	Index theory
19	11/13	7.1–7.2	Limit cycles
20	11/15	7.2–7.3	Lyapunov functions; Poincaré–Bendixson Theorem
21	11/20	9.2–9.3	The Lorenz equations (Lorenz's paper) (Matlab files)
22	11/27	10.0–10.1	One-dimensional maps
23	11/29	10.2–10.3	Logistic map
24	12/04	10.3–10.4	Periodic orbits of maps; Chaos (Matlab files)
25	12/06	10.5	Lyapunov exponent
26	12/11	11.1–11.4	Fractals

Course Policy and Grading

There will be a midterm exam in class and a final exam. The final grade will be computed according to:

Lecture Room:	115 Van Hise
Lecture Time:	9:30–10:45 TuTh
Lecturer:	Jean-Luc Thiffeault
Office:	503 Van Vleck
Email:
Office Hours:	Tue 12:15–13:00, Thu 8:30–9:15

Homework	35%
Midterm exam	30%
Final exam	35%

Midterm exam	Tue Oct 30, 2018 at 9:30–10:45	(in class)
Final exam	Thu Dec 20, 2018 at 14:45–16:45	(room SOC SCI 6203)

Math 415 Applied Dynamical Systems, Chaos and Modeling: Fall 2018

Final exam